Question

In uniform circular motion , V= r x omega
V is velocity or speed?
I have heard that velocity is variable and speed is fixed , but in this formula the velocity is fixed (r and omega not changing)
So v = r x omega is speed or velocity?

Answer 1

The difference is that velocity is a vector, that means it has a magnitude and a direction, while speed is only the magnitude of velocity. Sometimes both are changing (accelerated motion), sometimes velocity is the only one that changes (uniform circular motion), or sometimes neither are changing.

To understand your problem you need to see what your variables meen. If v means velocity ( a vector) then in you equation r is the position (a vector) and omega is the angular velocity (a magnitude). A vector times a magnitude is a vector. In this case velocity IS changing since the position of a fixed point in a circular motion is always changing so the r is not a constant.

On the other side, if v means speed (a magnitude), then r is the radius (the magnitude of the position vector) and omega is still the angular velocity (a magnitude). A magnitude time a magnitude gives a magnitude. In this case the speed is constant since the magnitude of the position vector is always the same: the radius of the circular trayectory.